Coherent signal analyzer

ABSTRACT

Systems and methods for analyzing a characteristic of a transmitter, a receiver, or a propagation channel are disclosed. At least one receiver signal resulting from at least one transmitter signal that has propagated through a propagation channel can be obtained. A first signal pair can be formed from a first receiver signal and a first transmitter signal, or from first and second receiver signals obtained from spatially-separated receiver antennas, or from first and second receiver signals which are attributable to different transmitter signals. Amplitude and phase information of a plurality of frequency components for each signal in the first signal pair can be determined. A set of comparison values for the first signal pair can be determined by comparing respective frequency component phases or respective frequency component amplitudes. A characteristic of the set of comparison values can then be analyzed.

STATEMENT REGARDING FEDERALLY SPONSORED R&D

This invention was made with government support under contractN00014-12-1-0539 awarded by the U.S. Office of Naval Research. Thegovernment has certain rights in the invention.

INCORPORATION BY REFERENCE TO ANY PRIORITY APPLICATIONS

Any and all applications for which a foreign or domestic priority claimis identified in the Application Data Sheet as filed with the presentapplication are hereby incorporated by reference under 37 CFR 1.57.

BACKGROUND

Field

This disclosure relates generally to systems and methods for analyzingsignals that have propagated from a transmitter to a receiver through achannel as waves in order to obtain information about the transmitter,the receiver, and/or the channel (including a target located in thechannel). More particularly, this disclosure relates to systems andmethods for performing coherent signal synthesis (at the transmitter)and/or analysis (at the receiver) to obtain information about thetransmitter, receiver, and/or a frequency-selective channel, such as amultipath channel.

Description of the Related Art

The propagation of waves, such as radio frequency (RF) waves, and theirbehavior when interacting with the world around us has long beenstudied. A practical application of this field of study has involvedtransmitting waves toward a target and then detecting those waves aftertheir interaction with the target as a means to learn information aboutthe target. Many systems and techniques have been developed for thispurpose. Nevertheless, there remains a need for new systems andtechniques for using transmitted and received signals to gaininformation about a transmitter, receiver, and/or propagation channel(including a target located in the channel).

SUMMARY

In some embodiments, a method for analyzing a characteristic of atransmitter, a receiver, or a propagation channel comprises: obtainingat least one receiver signal resulting from at least one transmittersignal that has propagated from the transmitter to the receiver throughthe propagation channel; forming at least a first signal pair whichcomprises a first receiver signal and a first transmitter signal, orfirst and second receiver signals which are obtained fromspatially-separated receiver antennas, or first and second receiversignals which are attributable to different transmitter signals;determining amplitude and phase information of a plurality of frequencycomponents for each signal in the first signal pair; determining a setof comparison values for the first signal pair by comparing respectivefrequency component phases or respective frequency component amplitudesof the signals in the first signal pair; and analyzing a characteristicof the set of comparison values.

In some embodiments, the method further comprises coherently receivingfirst and second receiver signals and/or coherently synthesizing firstand second transmitter signals.

In some embodiments, a system comprises: two or more receiver inputports and signal channels for obtaining two or more receiver signalsresulting from at least one transmitter signal that has propagatedthrough a propagation channel; and a processor configured to form atleast a first signal pair which comprises a first receiver signal and afirst transmitter signal, or first and second receiver signals which areobtained from spatially-separated receiver antennas, or first and secondreceiver signals which are attributable to different transmittersignals; determine amplitude and phase information of a plurality offrequency components for each signal in the first signal pair; determinea set of comparison values for the first signal pair by comparingrespective frequency component phases or respective frequency componentamplitudes of the signals in the first signal pair; and analyze acharacteristic of the set of comparison values.

The system can comprise receiver circuitry to coherently receive the twoor more receiver signals. The receiver circuitry may comprise a commonlocal oscillator to frequency down-convert the two or more receiversignals and/or one or more analog-to-digital converters to performsynchronous digital sampling of the two or more receiver signals. Thesystem can also comprise a transmitter with circuitry to coherentlysynthesize the two or more transmitter signals. The transmittercircuitry may comprise a common local oscillator to frequency up-convertthe two or more transmitter signals. In some embodiments, the systemcomprises a benchtop analyzer.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a radio frequency (RF) transmitter and receiveroperating in a multipath channel.

FIG. 2 illustrates a system for characterizing polarization modedispersion in signals measured at a receiver after propagating through achannel, such as a multipath channel.

FIG. 3A illustrates a system for analyzing atransmitter-channel-receiver system using one transmitting antenna andtwo spatially-separated receiving antennas.

FIG. 3B is a table which lists the signal pairs whose frequencycomponent phases and/or amplitudes can be compared to determine coherentsignal dispersion information for the system shown in FIG. 3A.

FIG. 4A illustrates a system for analyzing atransmitter-channel-receiver system using one transmitting antenna andtwo spatially-separated, dual polarized receiving antennas.

FIG. 4B is a table which lists the signal pairs whose frequencycomponent phases and/or amplitudes can be compared to determine coherentsignal dispersion information for the system shown in FIG. 4A.

FIG. 5A illustrates a system for analyzing atransmitter-channel-receiver system using one dual polarizedtransmitting antenna and two spatially-separated, dual polarizedreceiving antennas.

FIGS. 5B and 5C illustrate two separable transmitter signals which canbe used in the system shown in FIG. 5A.

FIG. 5D is a table which lists the signal pairs whose frequencycomponent phases and/or amplitudes can be compared to determine coherentsignal dispersion information for the system shown in FIG. 5A.

FIG. 6 illustrates an example method for conducting coherent signalanalysis using transmitted and received signals from, for example, thesystem of FIG. 5A.

FIG. 7 illustrates example coherent signal dispersion curves on asphere.

FIG. 8 is an example of a benchtop analyzer for performing the coherentsignal dispersion analyses described herein.

DETAILED DESCRIPTION

The systems and methods described herein are useful for analyzingsignals that have propagated from a transmitter to a receiver through afrequency-selective channel, such as a multipath channel, in order todetermine information about the transmitter, the receiver, and/or thechannel (including one or more targets located in the channel). Thesesystems and methods can take advantage of, for example, multipathpropagation effects that cause modified versions of a transmitted signalto arrive at the receiver after having traversed the multipath channel.(Such multipath propagation effects are discussed with respect to FIG.1.) These modified versions of the transmitted signals which aredetected at the receiver can be compared with one another and/or withthe original transmitted signals themselves in order to determineinformation about the transmitter, the receiver, and/or the channel.

FIG. 1 illustrates a radio frequency (RF) transmitter 110 and receiver120 operating in a multipath channel. The transmitter 110 includes anantenna T1 which transmits RF waves into the multipath channel. The RFwaves are received by the receiver antenna R1. The multipath channelincludes one or more targets 130, 132 which reflect, refract, diffract,scatter, or otherwise cause the transmitted radio waves to arrive at thereceiver antenna R1 along multiple paths.

In the illustrated example, RF waves from the transmitter antenna T1arrive at the receiver antenna R1 along a line of sight (LOS) pathwayand two other multipaths M₁ and M₂ which result from the presence of thetargets 130, 132. In some cases, the multipath effects introduced by thetargets 130, 132 can be time-varying. For example, a target in themultipath channel can be physically moving or it can have some othertime-varying characteristic which affects the RF waves received at thereceiver. The collective response consisting of effects from thetransmitter, the channel, and the receiver can be referred to as thesystem response, the system impulse response, the system transferfunction, the time varying system impulse response, the time-varyingsystem transfer function, etc.

In many applications, multipath signals are undesirable and are oftenconsidered to be an impairment. However, the systems and methodsdescribed herein can take advantage of multipath propagation effects (orother effects which occur in other types of frequency-selectivechannels) to detect changes in the propagation channel, includingchanges in one or more characteristics of the targets 130, 132.Multipath propagation effects can modify a transmitted signal in manyways, including by introducing (through scattering, reflection,refraction, diffraction, etc.) constructive or destructive interference,phase shifting, time delay, frequency shifting, and/or polarizationchanges to each multipath component. The systems and methods describedherein can use techniques for identifying, measuring, and/or otherwiseanalyzing any of these effects, or others, to gain information about themultipath channel, including the targets 130, 132 located in thechannel. It should be understood, however, that while variousembodiments in this application are described in the context ofmultipath propagation channels, the systems and techniques describedherein are also applicable to other types of frequency-selectivechannels. For example, the channel could be one in which one (or perhapsmore) path(s) are themselves frequency-selective, such as afrequency-selective medium or a frequency selective surface reflection.

In addition, besides being used to gain information about the channel(including one or more targets located in the channel), the systems andmethods described herein can also be used to gain information about thetransmitter and/or the receiver. For example, the systems and methodsdiscussed herein can be used to identify or characterize changes in thepolarization state of the transmitted signals, changes in theorientation or location of transmitter antennas, changes in acombination of signals from multiple transmitter antennas (e.g., changesin the amplitude and/or phase weighting factors applied to multipletransmitted signals), changes in the relative delays between transmittedsignals, etc. Similarly, the systems and methods discussed herein can beused to identify or characterize similar effects at the receiver. Any ofthese effects impacting the system response can be identified, measured,and/or otherwise analyzed to gain information about the transmitter, thereceiver, and/or the channel (including the targets 130, 132 located inthe channel).

Thus, the systems and methods described herein can characterize not onlythe channel but also the transmitter and/or receiver. For example, ifthe transmitter and receiver are fixed, then the measured signals can beused to characterize changes in the channel. But for a fixed channel anda fixed receiver, the measured signals can characterize changes in thelocation and/or properties of the transmitter. Similarly, for a fixedtransmitter and channel, the received signals can characterize changesin the location and/or properties of the receiver. Or, in general, themeasured signals can contain information about transmitter effects,channel effects, and receiver effects (which effects may or may not beseparable).

The received signal(s) represent the convolution of the transmittedsignal(s) with the channel, and hence is/are a function of thetransmitted signal. When the transmitted signal(s) is/are known, thatknowledge can be used by the receiver to estimate the system response,typically with greater accuracy than if the transmitter signal is notknown. This capability has an advantage of limiting the impacts due tothe specific waveforms that are transmitted, especially those exhibitingany time-varying spectral properties.

FIG. 2 illustrates a system 200 for characterizing polarization modedispersion in signals measured at a receiver after propagating through achannel, such as a multipath channel. The phenomenon referred to hereinas polarization mode dispersion can generally be understood as avariation in the polarization state of the received signal as a functionof the signal's frequency components (i.e., the polarization state(s)is/are altered distinctly for the different frequency components of thereceived signal(s)). Polarization mode dispersion can occur, forexample, in channels exhibiting both a delay spread between signalscarried by orthogonally-polarized waves and power coupling between thepolarization modes. One example of polarization mode dispersion is thatthe channel may couple vertically polarized waves into horizontallypolarized waves on paths with different delays relative to thevertically polarized path, possibly in a frequency-dependent fashion, orvice versa. For each polarization mode, the complex transfer functiongains (amplitude and phase) in the channel may exhibit distinctvariations as a function of frequency, leading to polarization modedispersion. The polarization mode dispersion can be introduced by thetransmitter, the channel, or the receiver. For example, polarizationmode dispersion can be caused by a frequency-selective channel, such asa multipath channel, or by intentionally-introduced polarization modedispersion at the transmitter, or can be introduced at the receiver byusing received signals that are delayed relative to each other.

The system 200 illustrated in FIG. 2 includes a transmitter 210 with apolarized transmitting antenna T1. The antenna T1 has x-polarization,which could arbitrarily be vertical, horizontal, right or left-handcircular, slant ±45°, etc. The system 200 also includes a receiver 220with a dual polarized receiving antenna R1. The dual polarized receivingantenna R1 is u-polarized and v-polarized, where u and v represent anypair of orthogonal polarizations, including vertical and horizontal,right and left-hand circular, slant +45° and slant −45°, etc. In someembodiments, either the u- or v-polarization is co-polarized with thex-polarization of the transmitting antenna T1, but this is not required.

The transmitter 210 transmits a signal S_(T1x) of bandwidth BW centeredat RF frequency f₀. One way to accomplish this is to generate a basebandsignal of bandwidth BW and to up-convert this signal to an RF carrierfrequency f₀. The resulting signal may be transmitted through thetransmitter antenna T1. Alternatively, the transmitter can transmit asignal consisting of at least two tones that are spaced apart infrequency, or the transmitter can sweep the frequency of a tone or pulsean RF tone. In some embodiments, a signal having a bandwidth BW centeredat the RF frequency f₀ can be directly generated using digital signalprocessing followed by digital-to-analog conversion. Other methods ofsignal generation are also possible.

The transmitted signal emitted from the transmitter antenna T1 beginspropagating through the multipath channel as x-polarized RF waves acrossthe full range of frequencies comprising the bandwidth BW of thetransmitted signal. In the case considered, the multipath channelincludes one or more targets 230 which introduce multipath contributionsat the receiver 220, which can result in a frequency-selective vectorpropagation channel (i.e., a frequency-selective channel for at leastone of the polarization modes) if path delays among the componentsexhibit sufficient spread. The receiving antenna R1 detectsorthogonally-polarized channel-modified versions of the transmitted RFsignal. The signal S_(R1u) represents the u-polarized component of thedetected signal, whereas the signal S_(R1v) represents the v-polarizedcomponent. These orthogonally-polarized signals can be processed at thereceiver 220 in order to determine information about the transmitter,the channel, and/or the receiver. If the transmitter and receiver arefixed, for example, then the received signals can be used to detect andcharacterize changes in the multipath channel. This is discussed in U.S.Patent Publication 2013/0332115, the entire contents of which are herebyincorporated by reference in this disclosure.

In some embodiments, the receiver 220 down-converts the received RFsignals and performs analog-to-digital conversion. The down-convertedsignals can be represented in any suitable form, including as in-phaseand quadrature signal components. The down-converted S_(R1u) and S_(R1v)signals can be analyzed sub-band by sub-band. For example, the receiver220 can perform an N-point fast Fourier transform (FFT), or othersuitable transform, to convert the signals into N bins in the frequencydomain. Each of these frequency bins can be considered as a sub-band(also referred to as a sub-frequency or sub-carrier). If, for example,the originally-transmitted baseband signal has a bandwidth of 20 MHz,the received S_(R1u) and S_(R1v) signals can divide the 20 MHz bandwidthinto any number of sub-bands which can then be considered independently,or in combination, to analyze the transmitter-channel-receiver system asa function of frequency.

In some embodiments, the receiver 220 calculates the polarization foreach sub-band by using the frequency-domain representations of thebaseband S_(R1u) and S_(R1v) signals to calculate a Jones vector orStokes parameters (which can be obtained by calculating the Jonescoherency matrix). These calculations are known in the art and examplesare provided in U.S. Patent Publication 2013/0332115, which areincorporated herein by reference. When calculated using signals from adual polarization (orthogonally-polarized) antenna, the result of thesecomputations is polarization state information. The polarizationinformation may be computed for each sub-band of the down-convertedbaseband signals received at the antenna R1. The polarization can bemeasured in a relative sense, or, if the orientation of the receiverantenna R1 is known, in an absolute sense. Polarization statistics, suchas the degree of polarization can also be measured for the entiresignal. Alternatively, repeated measurements of the state ofpolarization for each sub-band can be used to characterize the degree ofpolarization associated with the sub-band.

The polarization state information characterizes the polarization modedispersion—the frequency-dependency of the polarization modeshifting—caused by the channel or other factors. The polarization values(e.g., the Stokes parameters) for each sub-band can be normalized, wherethe S₁, S₂, and S₃ Stokes parameters are scaled to form a vector of unitmagnitude, depending upon whether or not the signal has a unity degreeof polarization. (Using a small enough sub-band spacing will generallyyield a degree of polarization near unity in each sub-band.) Theresulting polarization values may be plotted on or about a Poincarésphere as a visualization aid. For example, the normalized S₁, S₂, andS₃ Stokes parameters for each sub-band can be taken as coordinates andplotted on the Poincaré sphere (which has a unit radius) as a point.Each location on the Poincaré sphere corresponds to a differentpolarization state. When the Stokes parameters for multiple sub-bandsare plotted, the result is a locus of points which can be referred to asa polarization mode dispersion (PMD) curve. As discussed in U.S. PatentPublication 2013/0332115, PMD curves can be analyzed to determineinformation about the multipath channel. They may also provideinformation about any other type of frequency selective channel or aboutany portion of the transmitter-channel-receiver system.

While normalization of the S₁, S₂, and S₃ Stokes parameters to a unitvector may be advantageous in some embodiments, in other embodimentsretaining the amplitude information in the parameters is desirable, inwhich case the S₀ value will be maintained along with S₁, S₂, S₃. Theunnormalized parameters S₁, S₂, and S₃ taken from the full Stokes vector[S₀ S₁ S₂ S₃] can also be plotted in 3D space, but will not, in general,be confined to a locus that resides on a unit sphere, yet the resultingcurve may still be analyzed to determine information about thetransmitter-channel-receiver system. Also, it may also be useful toretain RF phase information of the signals used in the formation of theStokes parameters.

While FIG. 2 illustrates a system for analyzing polarization modedispersion, other system architectures and methods can be used toanalyze effects from the transmitter-channel-receiver system. Theseother system architectures and methods can yield valuable additionalinformation about any portion of the transmitter-channel-receiversystem. Examples of these other system architectures are illustrated inFIGS. 3A, 4A, and 5A.

FIG. 3A illustrates a system 300 for analyzing atransmitter-channel-receiver system using one transmitting antenna andtwo spatially-separated receiving antennas. The system 300 includes atransmitter 310 with a transmitting antenna T1. The transmitting antennaT1 can be arbitrarily polarized. The system 300 also includes a receiver320 with two spatially-separated receiving antennas R1, R2. In someembodiments, the receiving antennas R1, R2 are typically separated by atleast 0.5 wavelengths of the RF carrier frequency used by thetransmitter 310. The receiving antennas R1, R2 can each have arbitrarypolarization(s) that need not be the same as each other or the same asthe polarization of the transmitting antenna T1.

The transmitter 310 transmits a signal S_(T1) with a bandwidth BWcentered at an RF frequency f₀ via the antenna T1. The transmittersignal can be generated in any way disclosed herein, for example. Thesignal propagates through a frequency-selective channel, such as amultipath channel, with one or more targets 330 that create afrequency-selective response at the receiving antennas R1, R2. Thechannel, for example, can cause different modified versions of thetransmitted signal S_(T1) to be received at the spatially-separatedreceiving antennas R1, R2. The signal S_(R1) represents the signalreceived at R1, whereas the signal S_(R2) represents the signal receivedat R2. The receiver 320 can down-convert these signals and performanalog-to-digital conversion. As discussed further herein, the receivedsignals S_(R1) and S_(R2) can be coherently received (e.g., coherentlysampled and processed). In addition, the two receiver channels for thesesignals can be phase and/or gain matched.

Once, the S_(R1) and S_(R2) signals are down-converted and sampled, thefrequency component phases and amplitudes of the baseband S_(R1) andS_(R2) signals can be compared. This can be done in the time domain(e.g., via a filter bank) or in the frequency domain. For example, eachof the received signals can be converted into the frequency domain usingan N-point FFT operation. This operation divides the bandwidth of eachof the down-converted S_(R1) and S_(R2) signals into N frequency bins.The respective amplitudes and phases of the frequency components of theS_(R1) and S_(R2) signals can then be compared for each sub-band. Forexample, the amplitudes of the frequency components of one of thesignals can be compared to those of the other by calculating differencesbetween the respective amplitudes or ratios of the amplitudes.Similarly, the phases of the frequency components of one of the signalscan be compared to those of the other by calculating differences betweenthe respective phases. These are just some examples of computationswhich can be performed to compare the respective amplitudes and/orphases. Many others are also possible. For example, in some embodiments,the respective amplitudes and phases of the frequency components of theS_(R1) and S_(R2) signals can be compared by calculating a Jones vectoror Stokes parameters (normalized or unnormalized) for each sub-bandusing the S_(R1)/S_(R2) signal pair. Other mathematical computations canalso be used to compare the phases and/or amplitudes of the frequencycomponents of the two signals.

If the S_(R1) and S_(R2) signals had been obtained from a dual polarizedantenna, then the results of this computation would be polarizationinformation (as already discussed above with respect to FIG. 2).However, because the receiving antennas R1 and R2 are not substantiallyco-located, nor do they necessarily sample orthogonally-polarizedcomponents of the transmitted signal, the result of the Jones vector orStokes parameter computation does not quantify polarization. In fact,the resulting values do not describe any particular known physicalquantity. Nevertheless, the comparison of the respective amplitudeand/or phase of the signals received at spatially-separated antennas,for each frequency sub-band, can still provide useful information aboutthe transmitter-channel-receiver system. While the resulting values arenot polarization values, they can still be plotted for each sub-band onor about a unit sphere (similar to a Poincaré sphere) as a visualizationaid. (If normalization is applied, the signals will fall on a unitsphere, otherwise, in general they will not be confined to a unitsphere.) The resulting locus of points is not a polarization modedispersion (PMD) curve, however. Instead, the resulting curve can bereferred to as a coherent signal dispersion curve (CSDC). Furthermore,besides the received signals being compared with one another, theamplitudes and/or phases of the frequency components of the receivedsignals S_(R1) and S_(R2) can also be compared with those of theoriginal transmitted signal S_(T1). Again, this comparison of theamplitudes and/or phases of the frequency components of the receivedsignals with those of the original transmitted signal can be done on aper sub-band basis.

FIG. 3B is a table which lists the signal pairs whose frequencycomponent phases and/or amplitudes can be compared to determine coherentsignal dispersion information for the system 300 shown in FIG. 3A. Asalready discussed, the system 300 in FIG. 3A includes one transmitterchannel and two receiver channels that are obtained fromspatially-separated antennas. As shown in the table of FIG. 3B, thesystem provides three signal pairs whose respective frequency componentphases and/or amplitudes can be compared in order to determineinformation about the transmitter-channel-receiver system. Namely, therespective frequency component phases and/or amplitudes of the tworeceived signals S_(R1) and S_(R2) can be compared with one another.This is the first signal pair shown in the table in FIG. 3B. Inaddition, the respective frequency component phases and/or amplitudes ofthese two received signals S_(R1) and S_(R2) can also each be comparedwith those of the original transmitted signal S_(T1). These are thesecond and third signal pairs shown in the table in FIG. 3B. The system300 illustrated in FIG. 3A can therefore provide three coherent signaldispersion curves. Each of these curves can be analyzed, as discussedherein, to determine information about the transmitter, receiver, and/orchannel (including characteristics of one or more objects in thechannel).

As just mentioned, the respective frequency component amplitudes and/orphases of each of these signal pairs can be compared (e.g., for eachsub-band). (As already disclosed, one example of the comparison valuesthat can be calculated are the Stokes parameters for each sub-band ofeach signal pair. Stokes parameters (S₀, S₁, S₂, and S₃) for eachsub-band can be calculated according to the following equations:S₀=(Y₁·Y₁*)+(Y₂·Y₂*); S₁=(Y₁·Y₁*)−(Y₂·Y₂*); S₂=(Y₁·Y₂*)+(Y₂·Y₁*); andS₃=j(Y₁·Y₂*)−j(Y₂·Y₁*), where Y₁ is a complex number with amplitudeand/or phase information for a first signal in the pair of signals beingcompared and Y₂ is a complex number with amplitude and/or phaseinformation for a second signal in the pair of signals being compared.)The phases can be measured only in a relative sense with respect to oneanother or with respect to a local oscillator at the receiver 320.Alternatively, and/or additionally, the phases can be measured withrespect to a phase reference (e.g., a local oscillator) at thetransmitter 310. Frequency dispersion statistics (likened to degree ofpolarization) can be determined for each sub-band. Other computationsfor estimating the same or similar information can be calculated frompower measurements as described in Pratt et al., “A Modified XPCCharacterization for Polarimetric Channels,” IEEE Transactions onVehicular Technology, Vol. 60, No. 7, September 2011, p. 20904-2013.This reference describes polarization characterizations, but the sametechniques can be applied to the signals pairs disclosed herein eventhough they will not result in polarization information. This referenceis therefore incorporated by reference herein in its entirety for itsdisclosure of such analysis techniques.

In some embodiments, the receiver 320 can include more than tworeceiving antennas to obtain additional receiver signals. In addition,in some embodiments, the system 300 architecture can be reversed fromwhat is shown and can instead include two or more transmitter antennasfor sending two or more transmitter signals and only one receiverantenna for obtaining a receiver signal. (In embodiments with two ormore transmitter signals, the transmitter signals can be coherentlysynthesized, as discussed further herein.) Or the system 300 couldinclude two or more transmitter antennas (for sending two or moretransmitter signals) and two or more receiver antennas (for obtainingtwo or more receiver signals). In any case, all of the resulting signalpairs can be used to analyze the system, as disclosed herein.

FIG. 4A illustrates a system 400 for analyzing atransmitter-channel-receiver system using one transmitting antenna andtwo spatially-separated dual polarized receiving antennas. The system400 includes a transmitter 410 with a transmitting antenna T1. Thetransmitting antenna T1 can be arbitrarily polarized. The system 400also includes a receiver 420 with two spatially-separated receivingantennas R1, R2. In some embodiments, the receiving antennas R1, R2 aretypically separated by at least 0.5 wavelengths of the RF carrierfrequency used by the transmitter 410. The receiving antennas R1, R2 areboth dual polarized. The dual polarized receiving antenna R1 isu-polarized and v-polarized, where u and v represent any pair oforthogonal polarizations, including vertical and horizontal, right andleft-hand circular, slant +45° and slant −45°, etc. In some embodiments,either the u- or v-polarization is co-polarized with the polarization ofthe transmitting antenna T1, but this is not required. In someembodiments, the second dual polarized receiving antenna R2 is alsou-polarized and v-polarized. However, in other embodiments, theorthogonal polarizations of the second receiving antenna R2 can bedifferent than those of the first receiving antenna R1.

The transmitter 410 transmits a signal S_(T1) with a bandwidth BWcentered at an RF carrier frequency f₀ via the antenna T1. The signalS_(T1) can be generated using any technique disclosed herein or anyother suitable technique. The channel can include one or more targets430 which create one or more signal paths to the receiving antennas R1,R2. These signal paths result in frequency-selective propagation effectsthat typically cause different modified versions of the transmittedsignal S_(T1) to be received at the spatially-separated dual polarizedreceiving antennas R1, R2. The first receiving antenna R1 detectsorthogonally-polarized components of channel-modified versions of thetransmitted RF signal. The signal S_(R1u) represents the u-polarizedcomponent of the detected signal at the first receiving antenna R1,whereas the signal S_(R1v) represents the v-polarized component. Thesecond receiving antenna R2 likewise detects orthogonally-polarizedcomponents of channel-modified versions of the transmitted RF signal.The signal S_(R2u) represents the u-polarized component of the detectedsignal at the second receiving antenna R2, whereas the signal S_(R2v)represents the v-polarized component.

The orthogonally-polarized signal components from each of the receivingantennas R1, R2 can be processed at the receiver 420 in order todetermine information about the transmitter-channel-receiver system. Thereceiver 420 can down-convert these signals and performanalog-to-digital conversion. As discussed further herein, the receivedsignals S_(R1u), S_(R1v), S_(R2u), and S_(R2v) can be coherentlyreceived (e.g., coherently sampled and processed). In addition, the fourreceiver channels for these signals can be phase and/or gain matched.Once, the S_(R1u), S_(R1v), S_(R2u), and S_(R2v) signals aredown-converted and sampled, the frequency component phases andamplitudes of various signal pairs can be compared. The different signalpairs are described below with respect to FIG. 4B. Additionally, theabsolute frequency component phases and amplitudes for each signal paircan be measured (relative to some reference) and signal statistics suchas those comparable to degree of polarization can also be computed.

Each of the received signals S_(R1u), S_(R1v), S_(R2u), and S_(R2v) canbe converted into the frequency domain using an N-point FFT operation.This operation divides the bandwidth of each of the baseband S_(R1u),S_(R1v), S_(R2u), and S_(R2v) signals into N frequency bins. Therespective frequency component amplitudes and phases of the variouspairs of signals can then be compared for each sub-band using anycalculation discussed herein or any other suitable calculation. In someembodiments, the respective frequency component amplitudes and phasesfor a particular signal pair can be compared by, for example,calculating a Jones vector or Stokes parameters (normalized orunnormalized) for each sub-band. Additionally absolute phase andamplitude information and statistics can also be measured.

FIG. 4B is a table which lists the signal pairs whose frequencycomponent phases and/or amplitudes can be compared to determine coherentsignal dispersion information for the system 400 shown in FIG. 4A. Asalready discussed, the system 400 in FIG. 4A includes one transmitterchannel and four receiver channels, which are obtained fromspatially-separated, dual polarized antennas. As shown in the table ofFIG. 4B, the system 400 provides 10 signal pairs whose respectivefrequency component phases and/or amplitudes can be compared in order todetermine information about the transmitter-channel-receiver system. Thefirst six signal pairs are formed by the various combinations of thereceived signals S_(R1u), S_(R1v), S_(R2u), and S_(R2v). The firstsignal pair is made up of the RF signals detected at the first antennaR1. These are S_(R1u) and S_(R1v). The second signal pair is made up ofthe RF signals detected at the second antenna R2. These are S_(R2u) andS_(R2v). In both of these cases, polarization information can beobtained by comparing the phases and/or amplitudes of the signals ineach pair.

Additional information about the transmitter-channel-receiver system canbe obtained by also comparing respective frequency component phasesand/or amplitudes from signals detected at different antennas. A totalof four signal pairs can be formed to make these “cross-antenna”comparisons. These are signal pairs 3-6 in the table shown in FIG. 4B.They consist of the two u-polarization signals, S_(R1u) and S_(R2u); thetwo v-polarization signals, S_(R1v) and S_(R2v); the u-polarizationsignal from the first antenna and the v-polarization signal from thesecond antenna, S_(R1u) and S_(R2v); and finally the v-polarizationsignal from the first antenna and the u-polarization signal from thesecond antenna, S_(R1v) and S_(R2u). The values which result from thesecross-antenna comparisons of respective frequency component phasesand/or amplitudes (i.e., the values calculated from signal pairs 3-6 inthe table shown in FIG. 4B) are not polarization values. Nevertheless,they can include important information about thetransmitter-channel-receiver system (including effects due to one ormore objects within the channel).

The first six signal pairs in the table shown in FIG. 4B are made up ofonly the received signals. However, still additional information aboutthe transmitter-channel-receiver system can be obtained by comparingeach of the received signals S_(R1u), S_(R1v), S_(R2u), and S_(R2v) withthe original transmitted signal S_(T1). These are signal pairs 7-10shown in the table in FIG. 4B.

As discussed herein, the respective frequency component phases and/oramplitudes for each of the signal pairs from the table shown in FIG. 4Bcan be compared in a variety of ways. For example, this can be done foreach signal pair on a per sub-band basis by calculating a Jones vectoror Stokes parameters for each sub-band (e.g., using the equationsdisclosed herein). While the majority of the resulting calculated valuesare not polarization values, they can still be plotted on or about aunit sphere similar to a Poincaré sphere as a visualization aid. Two ofthe resulting ten curves are polarization mode dispersion (PMD) curves(i.e., those obtained from signal pairs 1 and 2 in the table of FIG.4B). The other eight curves can be described as coherent signaldispersion curves (CSDC) (i.e., those obtained from signal pairs 3-10 inthe table of FIG. 4B). Each of these curves can be analyzed, asdiscussed herein, to determine information about thetransmitter-channel-receiver system, including characteristics of one ormore objects in the channel. Additionally, absolute phase and/oramplitude information and statistics for each signal pair can also bemeasured.

In some embodiments, the receiver 420 can include more than two dualpolarized receiving antennas to obtain additional receiver signals. Inaddition, in some embodiments, the system 400 architecture can bereversed from what is shown and can instead include two or moretransmitter antennas (which can be spatially-separated and/or dualpolarized) for sending two or more transmitter signals and only onereceiver antenna (which can be dual polarized) for obtaining a receiversignal. Or the system 400 could include two or more transmitter antennas(for sending two or more transmitter signals) and two or more receiverantennas (for obtaining two or more receiver signals). In any case, allof the resulting signal pairs can be used to analyze the system, asdisclosed herein.

FIG. 5A illustrates a system 500 for analyzing atransmitter-channel-receiver system using one dual polarizedtransmitting antenna and two spatially-separated, dual polarizedreceiving antennas. The system 500 includes a transmitter 510 with atransmitting antenna T1 that is dual polarized. (Although the system 500is illustrated with a single transmitting antenna, multiplespatially-separated transmitting antennas could also be used.) The dualpolarized transmitting antenna T1 is x-polarized and y-polarized, wherex and y represent any pair of orthogonal polarizations, includingvertical and horizontal, right and left-hand circular, slant +45° andslant −45°, etc. The system 500 also includes a receiver 520 with twospatially-separated receiving antennas R1, R2. In some embodiments, thereceiving antennas R1, R2 are typically separated by at least 0.5wavelengths of the RF carrier frequency used by the transmitter 510. Thetwo receiving antennas R1, R2 can be dual polarized. The first dualpolarized receiving antenna R1 is u-polarized and v-polarized, where uand v represent any pair of orthogonal polarizations, including verticaland horizontal, right and left-hand circular, slant +45° and slant −45°,etc. In some embodiments, either the u- or v-polarization isco-polarized with the x- or y-polarization of the transmitting antennaT1, but this is not required. In some embodiments, the second dualpolarized receiving antenna R2 is also u-polarized and v-polarized.However, in other embodiments, the orthogonal polarizations of thesecond receiving antenna R2 can be different than those of the firstreceiving antenna R1.

The transmitter 510 includes two waveform generators 504 a, 504 b thatcan respectively provide baseband waveforms S_(T1x) and S_(T1y) that arecoherently synthesized and centered at a carrier frequency f₀ andtransmitted via the transmitting antenna T1. The waveform generators 504a, 504 b can provide any of the following waveforms: single tonecontinuous wave, wideband noise, band-limited noise, chirp, steppedfrequency, multi-tone, pulses, pulsed chirps, orthogonal frequencydivision multiplexing (OFDM), binary phase shift keying (BPSK), linearFM on pulse (LFMOP), etc. It should be understood, however, that theseare just example waveforms and that a wide variety of other waveformscan also be used, including any desired arbitrary waveform that may besuited to a given application. Each of the waveform generators 504 a,504 b can operate independently and can provide different waveforms atany given time. In some embodiments, the transmitted signals can bescaled and/or phase-shifted versions of one another. For example, whenusing a dual-polarized transmit channel, controlling the relative phaseand amplitude between the orthogonally-polarized channels leads tocontrol over the transmitted polarization state. In other embodiments,it is also possible to generate time-delayed signals, each with acontrolled relative scaling and/or shift between theorthogonally-polarized channels, for example to intentionally inducedispersion.

The baseband waveforms produced by the waveform generators 504 a, 504 bare provided to up-converters 502 a, 502 b to be centered at an RFcarrier frequency f₀. The RF carrier frequency is provided by the localoscillator 508. The carrier frequency is fed from the local oscillator508 to the up-converters 502 a, 502 b via signal lines 506 a, 506 b. Insome embodiments, the signal lines 506 a, 506 b are matched signal linesso as to maintain the phase coherency of the carrier frequency at theup-converters 502 a, 502 b. As shown in FIG. 5A, a single localoscillator 508 can feed both up-converters 502 a, 502 b. Alternatively,different local oscillators can respectively feed the up-converters 502a, 502 b. If different local oscillators are used, they are preferablysynchronized in phase and frequency. In some embodiments, thetransmitter 510 operates coherently such that the transmitted signalsS_(T1x) and S_(T1y) are coherently synthesized. FIG. 5A illustrates onesystem for coherently synthesizing transmit signals, but others can alsobe used. For example, the transmitter 510 can transmit a signalconsisting of two or more coherent continuous-wave or pulsed (orotherwise modulated) RF tones. Or two or more coherent signals can bedirectly generated using digital signal processing followed bydigital-to-analog conversion. Other methods of coherent signalgeneration are also possible.

As just discussed, in some embodiments, the transmitted signals arecoherent. Phase information can be preserved between the varioustransmitter signals. One way to achieve coherency between thetransmitted signals is to share a common local oscillator 508 used inthe up-conversion processing. A common local oscillator can beadvantageous in a multichannel transmitter because any impairments inthe local oscillator may affect all channels relatively equally, thusnot substantially affecting relative channel-to-channel comparisons. Insome instances, control over the local oscillator phase may beadvantageous, for example to assure that the starting phase referencefor each transmitted signal is substantially identical (or if notidentical then known so that the phase difference between transmittedsignals can be compensated). In some embodiments, the transmitter canadvantageously achieve precise control of the phase, amplitude,sampling, and frequency among the various generated signals used at thetransmitter. Further, in some embodiments, the phase noise of the localoscillator 508 is negligible such that energy of a desired signal in onesub-band coupling to an adjacent sub-band is significantly less (e.g.,two or more orders of magnitude less) than the signal being detected inthat adjacent band.

In addition, in some embodiments, each signal channel in the transmittercan be substantially phase and gain matched with the others. In order toachieve this matching, compensation circuits can be included. Forexample, if the transmitter includes different amplifier circuits ineach channel, then depending upon the transmit signal and the non-linearbehavior of the amplifier in each channel, it may be possible forasymmetrical signal distortion to occur (e.g., the effects on onechannel are not identical to the other channels). Such behavior could bedetrimental to a coherent, matched system, and so compensation circuitscan be used to reduce or minimize phase and gain mismatches in thechannels.

Although the transmitter 510 in FIG. 5A is shown in more detail than thetransmitters in preceding figures, each of the transmitters discussedherein can include elements and features similar to those discussed withrespect to the transmitter 510 to coherently synthesize transmitsignals.

In some embodiments, the transmitted signals S_(T1x) and S_(T1y) areadvantageously separable. This means that the transmitted signalsS_(T1x) and S_(T1y) have the property that they can be distinguishedfrom one another by the receiver 520. For example, the different signalsgenerated at the transmitter may be approximately orthogonal in somesense so that the signals can be separated at the receiver with littlecrosstalk among the signals. The multiple signals generated at thetransmitter can be sent using a different signal on each antenna, or byusing different linear combinations of multiple antennas to transmiteach signal. In addition, the transmitted signals can employ, forexample, a cyclic prefix to help reduce inter-symbol interference(non-orthogonal subcarriers).

The separability property of the transmitted signals can be achieved inseveral different ways, including, for example, through the use of timedivision multiplexing, frequency division multiplexing, and/or codedivision multiplexing. Methods based on eigendecomposition or singularvalue decomposition can also be used. Other methods may also bepossible. In the case of time division multiplexing, the signals S_(T1x)and S_(T1y) can be transmitted during different time slots such that thereceiver can distinguish the response of each of the receiving antennasto each of the transmitted signals. However, in many cases the system500 is used to detect a time-varying property of a multipath channel.Therefore, it may be desirable to transmit both of the signals S_(T1x)and S_(T1y) at the same or overlapping times in order to more completelycharacterize the time-varying property. This is particularly true if thevariations being monitored occur on a timescale that is short ascompared to the length of the time slots for the transmitted signals. Incases where it is desirable that the signals S_(T1x) and S_(T1y) betransmitted at the same time (or at time periods which overlap), thenfrequency division multiplexing, code division multiplexing,eigendecomposition, singular value decomposition, and/or other methodscan be used.

FIGS. 5B and 5C illustrate two separable transmitted signals which canbe used in the system shown in FIG. 5A. In the illustrated example, thetwo transmitted signals are separable based on frequency divisionmultiplexing. FIG. 5B shows an abstract representation of thetransmitted signal S_(T1x) in the frequency domain. The bandwidth (BW)of the signal S_(T1x) is shown as being separated into 8 segments. Theshaded regions indicate the frequency bands utilized by S_(T1x). In thiscase, S_(T1x) utilizes the odd frequency sub-bands (i.e., frequencysub-bands 1, 3, 5, and 7). Meanwhile, FIG. 5C shows an abstractrepresentation of the transmitted signal S_(T1y) in the frequencydomain. Once again, the bandwidth (BW) of the signal S_(T1y) is shown asbeing separated into eight segments and the shaded regions indicate thefrequency sub-bands utilized by S_(T1y). In this case, S_(T1y) utilizesthe even frequency sub-bands (i.e., frequency sub-bands 2, 4, 6, and 8).Because the signals S_(T1x) and S_(T1y) do not overlap in frequency, theresponse to each of these transmitted signals at the receiving antennascan be separately determined despite the fact that the signals may betransmitted at the same time. This separability property of thetransmitted signals S_(T1x) and S_(T1y) allows for significantenhancement in the number of signal pairs (and, hence, coherent signaldispersion curves) that can be obtained and analyzed in order tocharacterize the transmitter-channel-receiver system. It should beunderstood that FIGS. 5B and 5C illustrate just one idealized example ofa frequency division multiplexing scheme. Many others can be used.Further, although code division multiplexing is not illustrated, it toocan be used to transmit separable signals at the same or overlappingtimes.

The transmitter 510 transmits the separable baseband signals S_(T1x) andS_(T1y), up-converted to the RF carrier frequency, via the antenna T1.The S_(T1x) signal is transmitted via the x-polarized component of thetransmitting antenna T1, while the S_(T1y) signal is transmitted via they-polarized component of the transmitting antenna. (It is also possiblethat the signals can be transmitted using different weightedcombinations of the x- and y-polarization modes.) Thefrequency-selective channel (in this example, a multipath channel)includes one or more targets 530 which create multiple signal paths tothe receiving antennas R1, R2. These multiple signal paths result inmultipath propagation effects that cause different modified versions ofthe separable transmitted signals S_(T1x) and S_(T1y) to be received atthe spatially-separated, dual polarized receiving antennas R1, R2.

The first receiving antenna R1 detects orthogonally-polarized componentsof the received RF signals. The signal notation S_(R1u) ^(T1x) can beused to represent the u-polarized component of the detected signal atthe first receiving antenna R1 due to the transmitted signal S_(T1x),while the signal S_(R1v) ^(T1x) represents the v-polarized component ofthe detected signal at the first receiving antenna R1 due to thetransmitted signal S_(T1x). In this notation, for any given receivedsignal the subscript indicates the receiving antenna and polarizationchannel whereas the superscript indicates the transmitted signal whichexcited that particular received signal. Using this notation, the u- andv-polarization components detected at R1 due to the transmitted signalS_(T1y) can be written as S_(R1u) ^(T1y) and S_(R1v) ^(T1y),respectively. Similarly, the u- and v-polarization components detectedat R2 due to the transmitted signal S_(T1x) can be written as S_(R2u)^(T1x) and S_(R2v) ^(T1x), respectively. And the u- and v-polarizationcomponents detected at R2 due to the transmitted signal S_(T1y) can bewritten as S_(R2u) ^(T1y) and S_(R2v) ^(T1y), respectively.

These signals can be processed at the receiver 520 in order to determineinformation about the transmitter-channel-receiver system. Part of theprocessing that can be performed by the receiver 520 is separating thesignal responses at each of the four antenna inputs which areattributable to each of the transmitted signals S_(T1x) and S_(T1y). Forexample, the response at the u-polarization component of the firstreceiver antenna R1 will, in general, consist of a superposition ofchannel-modified versions of the transmitted signals S_(T1x) and S_(T1y)transmitted at both the x- and y-polarizations, respectively. The samewill generally be true of the response at the v-polarization componentof the first receiving antenna R1 and of the u- and v-polarizationcomponents of the second receiving antenna R2. The receiver 520 canperform signal separation operations to isolate the response at eachreceiver input that is attributable to each of the transmitted signals.

In the case where the transmitted signals S_(T1x) and S_(T1y) are madeseparable using frequency division multiplexing (as shown in FIGS. 5Band 5C), the respective signals S_(T1x) and S_(T1y) which are receivedat the u-polarization component of the first receiving antenna R1 can beobtained by isolating the frequency components respectively used by eachof the transmitted signals. The same can be done for the signalsreceived at the other three receiver inputs. Of course, the particularsignal separation operations that are performed will be dependent uponthe technique (e.g., time division multiplexing, frequency divisionmultiplexing, and/or code division multiplexing) used at the transmitter510 to make the transmitted signals separable. Techniques are known inthe art for separating signals which have been combined using thesemultiplexing techniques, as well as other techniques such aseigendecomposition or singular value decomposition techniques. Any suchseparation techniques can be employed by the receiver 520.

In summary, for cases where the transmitter 510 transmits multiplesignals, the detected response at each input port of the receiver 520will in general consist of the superposition of transmitter-, receiver-,and/or channel-modified versions of each of the multiple transmittedsignals (especially if the multiple transmitted signals are coincidentin time). The signal separation operations performed by the receiver 520isolate these superimposed signals in order to determine the individualresponse at each polarization component of each receiver antenna whichis attributable to each transmitted signal. In the case of the system500 in FIG. 5A, the outputs of the signal separation operations will bethe S_(R1u) ^(T1x), S_(R1v) ^(T1x), S_(R1u) ^(T1y), S_(R1v) ^(T1y),S_(R2u) ^(T1x), S_(R2v) ^(T1x), S_(R2u) ^(T1y), and S_(R2v) ^(T1y)signals. As discussed herein, the receiver 520 can coherently sample andprocess these signals to determine information about thetransmitter-channel-receiver system, including one or more targetslocated in the channel.

The receiver 520 can down-convert the S_(R1u) ^(T1x), S_(R1v) ^(T1x),S_(R1u) ^(T1y), S_(R1v) ^(T1y), S_(R2u) ^(T1x), S_(R2v) ^(T1x), S_(R2u)^(T1y), and S_(R2v) ^(T1y) signals and perform analog-to-digitalconversion. This is done using the down-converters 522 a-d and theanalog-to-digital converters 524 a-d. Each of these components can beconnected to, and controlled by, a common local oscillator 528 and/orclock signal (as applicable depending upon the circuitry) in order tomaintain consistent phase and/or timing references. For example, thesignals can be down-converted using a consistent phase reference and theanalog-to-digital converters can take synchronous samples. This helps toensure that relative phase information between the input signals ispreserved in the digitized signals. In addition, the signal lines 526a-d from the local oscillator 528 to these signal components can bematched so as to further help maintain phase coherency in the receiver.Although FIG. 5A illustrates a single local oscillator 528, multipleoscillators can be used if they are synchronized. The digital signalsthat are output from the analog-to-digital converters 524 a-d can besaved in a memory 540 and sent to a processor 550 for analysis. Thoughnot illustrated, the receiver 520 can also include signal conditioningcircuitry, such as amplifiers, filters, etc. In addition, the receiver520 could include an intermediate frequency (IF) processing stage.

In some embodiments, the received signals are coherently received andanalyzed. Phase information can be preserved between the variousreceived signals. For example, the received signals can share a commonlocal oscillator 528 used in the down-conversion processing and thesignals can be synchronously sampled during digital conversion.Coherence at the receiver may entail synchronization of the signalchannels in various forms, which can include: phase synchronization;frequency synchronization, sampling synchronization; and localoscillator synchronization in frequency, time, and/or phase. In someembodiments, the receiver 520 can also be coherent with the transmitter510. For example, the transmitter 510 and the receiver 520 could share acommon phase reference such as a local oscillator (e.g., as in amonostatic embodiment where the transmitter and receiver are housedtogether). (This can provide additional ways to characterize thetransmitter-channel-receiver system by enabling, for example, thecharacterization of Doppler spreads induced in the system.)Additionally, it may be desirable that the receiver signal channels aregain and phase matched (from the antennas to the analog-to-digitalconverters) across all frequency components of interest and that thelocal oscillator signal gains to each channel are substantially matched.In some embodiments, the receiver 520 can advantageously achieve precisecontrol of the phase, amplitude, sampling, and frequency among thevarious receiver channels.

As already mentioned, the receiver channels can be phase and/or gainmatched. In some cases, the phase and/or gain matching can bedynamically adjusted. This can be accomplished using phase shiftingelements and/or amplifiers in each receiver channel. In someembodiments, these phase shifting elements and/or amplifiers can beadjustable based on, for example, a calibration control input. Thecalibration control input can be obtained by passing a calibrationsignal through the various receiver processing channels. The effect ofeach processing channel on the calibration signal can then bedetermined. A calibration control input can be generated in order toreduce or eliminate differences between the effects that each processingchannel has on the calibration signal. For example, a calibrationcontrol input can be generated in order to reduce or eliminatedifferences between the respective gains of the receiver channels and/orto reduce or eliminate phase differences between the channels. Inaddition, the phase and/or gain matching can be temperature compensatedto help reduce phase and/or gain mismatches which may be induced atdifferent operating temperatures. Digital compensation of the digitizedsignals can also be employed to achieve phase and/or gain matching.

Although the receiver 520 in FIG. 5A is shown in more detail than thereceivers in preceding figures, each of the receivers discussed hereincan include elements and features similar to those discussed withrespect to the receiver 520 in order to coherently receive and analyzethe received signals.

Once, the S_(R1u) ^(T1x), S_(R1v) ^(T1x), S_(R1u) ^(T1y), S_(R1v)^(T1y), S_(R2u) ^(T1x), S_(R2v) ^(T1x), S_(R2u) ^(T1y), and S_(R2v)^(T1y) signals are down-converted and sampled, the respective frequencycomponent phases and amplitudes for various signal pairs can be comparedas a means of learning information about thetransmitter-channel-receiver system. The different signal pairs aredescribed below with respect to FIG. 5D.

FIG. 5D is a table which lists the signal pairs whose frequencycomponent phases and/or amplitudes can be compared to determine coherentsignal dispersion information for the system 500 shown in FIG. 5A. Asalready discussed, the system 500 in FIG. 5A includes two transmitterchannels (from one dual polarized transmitting antenna) and fourreceiver channels (which are obtained from spatially-separated dualpolarized antennas). As shown in the table of FIG. 5D, the system 500provides as many as 44 signal pairs whose respective frequency componentphases and/or amplitudes can be compared in order to determineinformation about the transmitter-channel-receiver system.

The first six signal pairs in FIG. 5D are formed by the variouscombinations of the received signals at the first and second receiverantennas R1, R2 which are attributable to the first transmitted signal,S_(T1x). These are S_(R1u) ^(T1x), S_(R1v) ^(T1x), S_(R2u) ^(T1x), andS_(R2v) ^(T1x). Signal pairs 1-2 are each made up oforthogonally-polarized components detected at a single one of thereceiving antennas R1, R2. In both of these cases, polarizationinformation can be obtained by comparing the respective frequencycomponent phases and/or amplitudes for the signals in each pair.

Additional non-polarization information about the multipath channel canbe obtained by also comparing respective frequency component phasesand/or amplitudes from signals detected at different antennas. Signalpairs 3-6 in FIG. 5D can be formed to make these cross-antennacomparisons. They consist of the two u-polarization signals that resultfrom the first transmitted signal S_(T1x), which are S_(R1u) ^(T1x) andS_(R2u) ^(T1x); the two v-polarization signals that result from thefirst transmitted signal S_(T1x), which are S_(R1u) ^(T1x) and S_(R2v)^(T1x); the u-polarization signal from the first antenna and thev-polarization signal from the second antenna that result from the firsttransmitted signal S_(T1x), which are S_(R1u) ^(T1x) and S_(R2v) ^(T1x);and finally the v-polarization signal from the first antenna and theu-polarization signal from the second antenna that result from the firsttransmitted signal S_(T1x), which are S_(R1v) ^(T1x) and S_(R2u) ^(T1x).The values which result from these cross-antenna comparisons of therespective frequency component phases and/or amplitudes of receivedsignals resulting from the same transmitted signal S_(T1x) (i.e., thevalues calculated from signal pairs 3-6 in the table shown in FIG. 5D)are not polarization values. Nevertheless, they can include importantinformation about the transmitter-channel-receiver system, including oneor more objects within the channel.

The second six signal pairs in FIG. 5D are formed by the variouscombinations of the received signals at the first and second receiverantennas R1, R2 which are attributable to the second transmitted signal,S_(T1y). These are S_(R1u) ^(T1y), S_(R1v) ^(T1y), S_(R2u) ^(T1y), andS_(R2v) ^(T1y). Co-antenna signal pairs are those made up oforthogonally-polarized components detected at a single one of thereceiving antennas R1, R2. These are signal pairs 7 and 8 in FIG. 5D.Comparisons of the respective frequency component phases and/oramplitudes for these signal pairs can yield polarization information.However, additional, non-polarization information can also be obtainedfrom the cross-antenna signal pairs. These are signal pairs 9-12 in FIG.5D.

The next 16 signal pairs in FIG. 5D (i.e., signal pairs 13-28) areformed by separately pairing each of the four received signalsattributable to the first transmitted signal (i.e., S_(R1u) ^(T1x),S_(R1v) ^(T1x), S_(R2u) ^(T1x), S_(R2v) ^(T1x)) with each of the fourreceived signals attributable to the second transmitted signal (i.e.,S_(R1u) ^(T1y), S_(R1v) ^(T1y), S_(R2u) ^(T1y), and S_(R2v) ^(T1y)).Specifically, signal pairs 13-16 represent the comparison of theu-polarization component detected at the first receiving antenna R1 dueto the first transmitted signal S_(T1x) with each of the receivedsignals (detected at both the first and second receiving antennas R1,R2) that are attributable to the second transmitted signal S_(T1y).Signal pairs 17-20 represent the comparison of the v-polarizationcomponent detected at the first receiving antenna R1 due to the firsttransmitted signal S_(T1x) with each of the received signals (detectedat both the first and second receiving antennas R1, R2) that areattributable to the second transmitted signal S_(T1y). Signal pairs21-24 represent the comparison of the u-polarization component detectedat the second receiving antenna R2 due to the first transmitted signalS_(T1x) with each of the received signals (detected at both the firstand second receiving antennas R1, R2) that are attributable to thesecond transmitted signal S_(T1y). Finally, signal pairs 25-28 representthe comparison of the v-polarization component detected at the secondreceiving antenna R2 due to the first transmitted signal S_(T1x) witheach of the received signals (detected at both the first and secondreceiving antennas R1, R2) that are attributable to the secondtransmitted signal S_(T1y). Thus, each of these signal pairs representswhat can be termed a “cross-transmitted signal” comparison. But some areco-antenna, cross-transmitted signal comparisons, while others arecross-antenna, cross-transmitted signal comparisons. None of thesesignal pairs yields polarization information when the respectivefrequency component amplitudes and/or phases are compared. Nevertheless,they can yield useful information about the transmitter-channel-receiversystem, including a target located in the channel.

The first 28 signal pairs in the table shown in FIG. 5D are made up ofonly the received signals. However, still additional non-polarizationinformation about the multipath channel can be obtained by comparingeach of the eight received signals S_(R1u) ^(T1x), S_(R1v) ^(T1x),S_(R1u) ^(T1y), S_(R1v) ^(T1y), S_(R2u) ^(T1x), S_(R2v) ^(T1x), S_(R2u)^(T1y), and S_(R2v) ^(T1y) with each of the two original transmittedsignals S_(T1x) and S_(T1y). These are signal pairs 29-44 shown in thetable in FIG. 5D. Specifically, signal pairs 29-32 represent thecomparison of the first transmitted signal S_(T1x) with each of the fourreceived signals that are attributable to it (i.e., S_(R1u) ^(T1x),S_(R1v) ^(T1x), S_(R2u) ^(T1x), and S_(R2v) ^(T1x)). Signal pairs 33-36represent the comparison of the first transmitted signal S_(T1x) witheach of the four received signals that are attributable to the othertransmitted signal S_(T1y) (i.e., S_(R1u) ^(T1y), S_(R1v) ^(T1y),S_(R2u) ^(T1y), and S_(R2v) ^(T1y)). Signal pairs 37-40 represent thecomparison of the second transmitted signal S_(T1y) with each of thefour received signals that are attributable to the other transmittedsignal S_(T1x) (i.e., S_(R1u) ^(T1x), S_(R1v) ^(T1x), S_(R2u) ^(T1x),and S_(R2v) ^(T1x)). Finally, signal pairs 41-44 represent thecomparison of the second transmitted signal S_(T1y) with each of thefour received signals that are attributable to it (i.e., S_(R1u) ^(T1y),S_(R1v) ^(T1y), S_(R2u) ^(T1y), and S_(R2v) ^(T1y)).

While FIG. 5A illustrates a system 500 with two transmitter channelsfrom a single dual polarization antenna, the two transmitter channelscould alternatively be connected to two spatially-separated antennas. Infact, the system could include an arbitrary number ofspatially-separated transmitter antennas, and each of those could bedual polarized to provide two transmitter channels each. Further, whilethe system 500 illustrated in FIG. 5A includes two receiver antennas, itcould include any arbitrary number of spatially-separated receiverantennas, including a single receiver antenna. Again, each of thosecould be dual polarized to provide two receiver channels each. Systemswith larger numbers of transmitter and receiver channels can providelarger numbers of coherent signal dispersion curves. For example, afour-transmitter-channel by four-receiver-channel system could provideover 100 coherent signal dispersion curves for analysis. It should beunderstood, however, that systems such as those illustrated herein caninclude an arbitrary number of coherent transmitter channels and anarbitrary number of coherent receiver channels. In addition,tri-polarized antennas could be used by the transmitter and/or receiverso as to allow for the transmission or reception of electric fields fromany direction.

While separate transmitter and/or receiver signals have been describedherein as being associated with the individual outputs of separateantenna ports, it is not required that each transmitted signalcorrespond only to what is sent via a single antenna or that eachreceived signal correspond only to what is received via a singleantenna. For example, instead of employing antenna ports as thefundamental quantity, beams derived from a weighted combination ofantenna elements (on the transmitter and/or receiver side) can be usedinstead. In such cases, each beam can be treated as one of thetransmitter/receiver signals for purposes of the analysis describedherein. This is one of the benefits of a coherent system. In fact, thesebeams can even be frequency dependent. For a linear combination ofspatially-separated antennas, frequency-dependent weights couldcorrespond to different beam steering directions as a function offrequency. For linear combinations of a single dual polarized antenna,frequency-dependent weights would generally correspond to differentpolarizations as a function of frequency. For an antenna system withboth space and polarization separated elements, a weighted combinationinvolving space and polarization dimensions can be used.

While FIGS. 1, 2A, 3A, 4A, and 5A all illustrate bistatictransmitter/receiver configurations, in other embodiments, they couldeach be monostatic configurations. Furthermore, although thetransmitters and receivers have been described herein as each usingdifferent antennas, one or more antennas could be shared in common byboth a transmitter and a receiver (e.g., as in a monostatic system). Forthese cases, to improve isolation between the transmitter and thereceiver when operating simultaneously, a circulator (or other circuitto mitigate the impact of transmissions on the receiver) can beemployed. In the case that multiple separable transmitter signals areemployed, although each receiver signal will be subject to interferencefrom the transmitter signal coupled to the common antenna (attenuated bythe isolation circuit), the signals of interest from the othertransmitter signals can be orthogonal, thereby facilitating reception ofseparable signals at the receiver.

In addition, although FIGS. 2, 3A, 4A, and 5A use RF signals to make themeasurements described herein, it should be understood that the conceptscan equally apply to other types of signals, including signals carriedby various types of electromagnetic radiation such as infrared orvisible light signals, ultraviolet signals, or x-ray signals. Inaddition, the concepts described herein can apply to transmission linesor to signals carried by other types of wave phenomena besideselectromagnetism, such as acoustic signals, etc. Furthermore, in placeof, or in addition to antennas to measure the electric field,alternative sensors could be employed to measure the magnetic field.Thus, the systems described herein can be adapted to operate usingdifferent types of signals.

FIG. 6 illustrates an example method 600 for conducting coherent signalanalysis using transmitted and received signals from, for example, thesystem 500 of FIG. 5A. The method 600 begins at block 610 where multipletransmit signals are coherently synthesized, for example as discussedwith respect to FIG. 5A. These transmit signals can be sent through achannel to a receiver (e.g., receiver 520). At block 620, multiplesignals are received after having propagated through a channel, such asa multipath channel. The signals can be received using two or morespatially-separated receiver antennas. The receiver antennas can be dualpolarized. The received signals can result from one or more transmittedsignals (e.g., using transmitter 510). The received signals can becoherently received and analyzed (e.g., coherently down-converted andsynchronously sampled), for example as discussed with respect to FIG.5A. In the case where the received signals result from multipleseparable transmitted signals, this processing can include performingsignal separation operations to isolate the received signals that areattributable to each transmitted signal. The coherent sampling andprocessing preferably preserves phase information between the variousreceived signals. In addition, if a phase reference is shared betweenboth the transmitter and receiver (as would be possible using a sharedlocal oscillator in a monostatic configuration), then phase informationcan be preserved between transmitted and received signals.

At block 630, the transmitted and received signals from blocks 610 and620 can each be separated into frequency sub-bands. This can be doneusing, for example, a Fourier transform or other processing.

At block 640, multiple pairs of received and transmitted signals areformed. FIG. 5D illustrates examples of these signal pairs. In general,the signal pairs can be formed between received signals only, or betweenreceived signals and transmitted signals. When signal pairs betweenreceived signals and transmitted signals are formed, these can includepairs which include a received signal and the particular transmittedsignal to which the received signal is attributable, or pairs whichinclude a received signal and a transmitted signal other than the one towhich the received signal is attributable. Signal pairs can be formedbetween received signals detected at the same antenna or at differentantennas. Signal pairs can be formed between received signals that havethe same polarization or different polarizations. In addition, signalpairs can be formed between received signals that are attributable tothe same transmitted signal or between received signals that areattributable to different transmitted signals.

At block 650, frequency component phase and/or amplitude comparison datacan be calculated for each signal pair from block 640 and for eachfrequency sub-band from block 630. For example, the amplitudes of thefrequency components of one of the signals can be compared to those ofthe other by calculating differences between the respective amplitudesor ratios of the amplitudes. Similarly, the phases of the frequencycomponents of one of the signals can be compared to those of the otherby calculating differences between the respective phases. Othercomputations can also be useful in comparing these magnitudes andphases. For example, in some embodiments, calculation of the phaseand/or amplitude comparison data is accomplished by calculating a Jonesvector or Stokes parameters (normalized or unnormalized) for eachsub-band of each signal pair. (Again Stokes parameters (S₀, S₁, S₂, andS₃) for each sub-band can be calculated according to the followingequations: S₀=(Y₁·Y₁*)+(Y₂·Y₂*); S₁=(Y₁·Y₁*)−(Y₂·Y₂*);S₂=(Y₁·Y₂*)+(Y₂·Y₁*); and S₃=j(Y₁·Y₂*)−j(Y₂·Y₁*), where Y₁ is a complexnumber with amplitude and/or phase information for a first signal in thepair of signals being compared and Y₂ is a complex number with amplitudeand/or phase information for a second signal in the pair of signalsbeing compared.) Although these computations are traditionally used todetermine polarization states, they can also be applied as an analyticaltool even in cases where the signal pairs are such that the computationsdo not result in polarization information. As discussed herein, the setof per sub-band comparison values for each signal pair can be referredto as a coherent signal dispersion (CSD) curve or a polarization modedispersion (PMD) curve, depending on the particular signal pair.

As just mentioned, for each signal pair obtained from any systemarchitecture described herein, Jones vectors or Stokes vectors can beformed. The representation for the former can be written as a complexscale factor (amplitude and phase) that multiplies a unit Jones vector.If relative amplitude and relative phase alone are of interest (such asin characterizing polarization states on a unit sphere), the complexscale factor can be ignored, although the amplitude and phaseinformation provided by the complex scale factor can potentially beuseful for sensing and other applications. Stokes vectors of the form[S₀ S₁ S₂ S₃] can be formed for each signal pair using, for example, theequations provided herein. This unnormalized form of a Stokes vector mayor may not have a degree of polarization of unity (i.e., where thesquare of S₀ equals the sum of the squares of S₁, S₂, and S₃). In someembodiments, however, the sub-band spacing can be chosen so that thedegree of polarization is near unity. In some cases, it may beappropriate to normalize the [S₁ S₂ S₃] vector (e.g., so that the sum ofthe squares of S₁, S₂, and S₃ equals the square of S₀, which essentially“forces” the condition of having unit degree of polarization). Whenplotting the CSD or PMD curves in any of these cases, the 3D locus willnot be constrained to a unit sphere, but in some cases, it may useful tonormalize the [S₁ S₂ S₃] vectors to have unit magnitude so that the CSDor PMD curves will be constrained to a unit sphere. In the case of PMD,this is equivalent to considering the polarization state (i.e., therelative amplitude and relative phase between the signals associatedwith the signal pair). Since these representations deal primarily withrelative amplitude and relative phase information, some amplitude andphase information (a complex scale factor) is not retained through thisrepresentation. For all of the cases, it may be useful to retainamplitude and/or phase information associated with the signal pairs thatmight otherwise be lost in a particular representation. The amplitudeand phase can be relative to some reference used to measure thesevalues.

Calculation of a set of Stokes parameters for each sub-band results in aStokes vector for each sub-band. (Again, although the same equations maybe used for calculating Stokes vectors for CSD signal pairs as for PMDsignal pairs, the Stokes vectors for CSD signal pairs do not consist ofpolarization information). If the Stokes vectors (and hence the curves)are not normalized to unit magnitude, the vectors contain amplitudeinformation (e.g., the S₀ term in the Stokes vector provides amplitudeinformation) that can be utilized in addition to phase information toanalyze the signals. The resultant CSD (or PMD) curve fromnon-normalized Stokes vectors would not necessarily be constrained toreside on a unit sphere. In some cases, CSD and PMD curves may becontinuous. However, in some cases, the resulting curve is a locus ofpoints that may not be continuous. For example, if the transmitpolarization is varied with sub-band, or more generally, if the relativeamplitude and phase between transmit ports is varied with sub-band, theresulting curve may exhibit discontinuities.

For each signal pair, frequency component amplitude and/or phasecomparisons can be made between the signals for different relativedelays (e.g., where one of the signals is delayed by one or moresamples), or for different frequency offsets (for example where thesubcarriers of the two signals are not the same, but are intentionallyoffset). These offsets in delay and frequency can also be consideredsimultaneously (e.g., offsets in delay and in frequency). Suchcharacterizations may be useful to establish decorrelation times anddecorrelation frequencies. Furthermore, a signal pair consisting of areceiver signal and a transmitter signal could use a delay differencefor the signals to align them in time for comparison purposes. Signalcross-correlation, for example, could be used to identify the delay thatshould be used to align the transmitter signal with the receiver signal.

Dynamic CSD curves can be determined by applying the just-describedtechnique repeatedly over time. This can be done by extracting a timewindow of data of a desired length from the pairs ofreceived/transmitted signals. Then, for each time window, the frequencycomponent phase and/or amplitude comparison data can be calculated foreach frequency sub-band. The time window can then be advanced and theper sub-band comparison values can be calculated once again. Thisprocess can be repeated as long as desired in order to determine thetime domain behavior of the CSD curves. The length of the time windowfor each of these iterations can be selected, for example, based uponthe timescale of the time-varying effects that are to be analyzed.

At block 660, the frequency component phase and/or amplitude comparisondata (e.g., coherent signal dispersion (CSD) curves) from block 650 canbe analyzed in order to determine a characteristic of the transmitter,receiver, and/or channel, including a characteristic of a target locatedin the channel. In some embodiments, this analysis can includevisualization by plotting the per sub-band comparison data for eachsignal pair on or about a sphere or other manifold. FIG. 7 illustratesexample coherent signal dispersion curves 710, 720, 730 on a sphere 700.As previously discussed herein, a Poincaré sphere traditionally has beenused to visualize polarization states. Each point on the Poincaré spheretraditionally corresponds to a different polarization state. And pointson opposite sides of the sphere traditionally correspond to orthogonalpolarization states. However for signal pairs that do not yieldpolarization information, the representations correspond to a differentquantity. Notwithstanding the fact that the coherent signal dispersioncurves 710, 720, 730 described herein do not relate to polarizationinformation, they can still be plotted on or about a unit sphere similarto a Poincaré sphere 700 as a useful visualization technique.

The analysis in block 660 can include identifying a characteristic ofthe comparison data from block 660 at a given time (e.g., length, shape,location on the sphere of a CSD curve, etc.). A characteristic ofinterest can be identified by, for example, relating the comparison datato calibration data or previously-elicited comparison data.Additionally, the analysis can include identifying a change in acharacteristic of the comparison data as a function of time (e.g.,length, shape, location on the sphere of a CSD curve, etc.). Acharacteristic of the comparison data may correspond to a physicalcharacteristic of the system. For example, the length of a CSD curve maybe reflective of temporal dispersion between channels; the complexity ofa CSD curve may be indicative of the multipath composition; and periodicoscillations may reflect periodic processes in thetransmitter-channel-receiver system. Any of these properties, or others,of the comparison data can be analyzed. These analyses can be conductedin the time domain, spatial domain, and/or frequency domain. Forexample, assume that a target within the channel vibrates at afrequency, f_(v), while the transmitter and receiver are heldstationary. A spectral analysis, perhaps via a discrete Fouriertransform, of one or more of the dynamic Stokes parameters calculatedfrom PMD or CSD data should indicate the presence of a frequencycomponent at f_(v). The magnitude of this f_(v) component along with thepossible presence of other frequency components could provide usefulinformation about said vibrating target. Thus, the spectral analysis caninclude, for example, determining the magnitude(s) of one or morespectral components of the comparison data from block 660. Manytechniques are disclosed in U.S. Patent Publication 2013/0332115 foranalyzing polarization mode dispersion curves to obtain usefulinformation about a multipath channel. Notwithstanding the distinctionsbetween polarization mode dispersion curves and coherent signaldispersion curves, the same PMD curve analysis techniques can be appliedto the CSD curves disclosed herein. Therefore, U.S. Patent Publication2013/0332115 is incorporated by reference herein in its entirety for itsdisclosure of such analysis techniques.

Various operations that can be performed on the coherent signaldispersion curves as part of these analyses include filtering,averaging, statistical analyses, excision, integration, rotation,smoothing, correlation, eigendecomposition, Fourier analyses, and manyothers.

For some analyses it may be advantageous to reduce each coherent signaldispersion curve to a single value that represents the curve as a whole.This can be done using, for example, a centroiding operation.Experiments have shown that the centroid of a coherent signal dispersioncurve can efficiently and effectively reduce unwanted noise while stillproviding useful information about the transmitter-channel-receiversystem.

Estimation techniques can be applied in order to reduce variations in ameasured CSD curve. This can be done because there typically is acorrelation between the values for neighboring sub-bands in the curve(i.e., the coherence signal dispersion information is not generallyexpected to exhibit discontinuities from one sub-band to the next). Thisproperty of coherent signal dispersion curves allow for the usage oftechniques to improve the quality of CSD curve estimates.

CSD curves are believed to be dependent to a significant degree on thetransmitter-channel-receiver system, including the state of any targetswithin the channel. (The CSD curves may be dependent to a lesserdegree—potentially a far lesser degree—on the specific content orproperties of the transmitted signals, for example, so long as thetransmitted signals have adequate signal strength across the bandwidthbeing analyzed.) In other words, the CSD curves are believed to bestrongly dependent on the factors impacting the transmitter (such astransmit antenna location/motion, transmit polarization, beam pattern,etc), the receiver (such as receiver antenna location/motion and beampattern), and factors leading to the channel response. The CSD curveswill change in response to physical changes in the frequency-selectiveenvironment, including physical movement of scatterer targets inrelation to the locations of transmitting and receiving antennas. Thismeans that characteristics of the CSD curves at a given moment in timemay be used to identify a specific multipath channel, including aspecific state of a target located in the channel, potentially withoutknowledge of the transmitted signal(s) that produced the CSD curves.

One application of this property is that the transmitted signal(s) neednot necessarily be known in order to determine useful information abouta target located in the channel. Instead, a signal of opportunity can beused as the transmitted signal. Signals of opportunity could include,for example, cellular telephone signals, Wi-Fi signals from an Internethotspot, and many others. These signals can be received and analyzedusing the systems and techniques discussed herein to learn informationabout, for example, a target located in the environment. One specificapplication which could entail the use of a signal of opportunity is asystem for measuring a patient's heart or respiration rate in a hospitalor other clinical environment. Such environments typically have strictregulations regarding the transmission of wireless signals. Thus, itcould be advantageous if the system did not require its own transmitterbut could instead make use of unknown existing signals of opportunity.The system could generate one or more CSD curves by receiving andprocessing those existing transmitted signals, as discussed herein. Ifthe patient's heart or lungs are present in the propagation channelbetween the receiver and the unknown transmitted signals of opportunity,then one or more of the CSD curves will likely include information aboutthe rate of movement of the heart or lungs. This rate of movement can bedetermined by, for example, analyzing the frequency content of the CSDinformation.

Another application of the CSD analysis described herein relates tomonitoring the movements of, for example, mechanical machinery. In thecase of fixed transmit and receive antennas, such movements, even ifthey are small vibrations, can result in changes to the multipathwireless environment of the object. As already noted, these changes inthe multipath environment can lead to corresponding changes to the CSDcurves that are detected using the systems and methods described herein.Changes in the CSD curves can be analyzed in order to monitor the normaloperation of the machinery or even detect irregular operation, such asnew or different vibrations. Take the example of a three-blade fan. Therotational frequency of the fan can be determined from the CSD curvesbecause they will vary at a rate that corresponds to the rotationalfrequency of the fan. Further, if a ball bearing begins to fail, or oneof the fan blades becomes damaged, this will induce a change in thevibrations that can also be detected by monitoring changes in the CSDcurves. Many techniques are disclosed in U.S. Patent Publication2013/0332115 for analyzing polarization mode dispersion curves to obtainuseful information about such physical movements of a target object.Notwithstanding the distinctions between polarization mode dispersioncurves and coherent signal dispersion curves, the same PMD curveanalysis techniques can be applied to the CSD curves disclosed herein.Therefore, U.S. Patent Publication 2013/0332115 is incorporated byreference herein in its entirety for its disclosure of such analysistechniques.

One benefit of the CSD curves described herein over the PMD curvesdescribed in U.S. Patent Publication 2013/0332115 is the rich diversityof the CSD curves, which far outnumber PMD curves. Owing to the richdiversity of the CSD curves, it becomes much more likely that a giventime-varying characteristic of the multipath channel, including a targetobject in the channel, will be evident in at least one of the CSDcurves.

U.S. Patent Publication 2013/0332115 describes many other practicalapplications of PMD analysis. It should be understood that the systemsand methods described herein for performing CSD can also be applied toany of those applications, likely with improved results. Thus, U.S.Patent Publication 2013/0332115 is incorporated by reference herein forits disclosure of all such practical applications.

FIG. 8 is an example of a benchtop analyzer 800 for performing thecoherent signal dispersion analyses described herein. The benchtopanalyzer 800 can enable measurement and analysis of polarization modedispersion curves and coherent signal dispersion curves, as discussedherein. The illustrated embodiment operates using RF signals, thoughsignals carried by other types of waves can also be used. The benchtopanalyzer 800 can include only a receiver (e.g., 520), only a transmitter(e.g., 510), or both a transmitter (e.g., 510) and a receiver (e.g.,520).

The benchtop analyzer 800 can enable measurement and characterization ofPMD and CSD signatures in both laboratory and field applications. Thesemay include, but are not limited to, the following: signaturemeasurement for wireless security; vibration measurement systems;surface roughness characterizations; multipath characterization; changedetection; form change sensing; translational motion sensing; dielectricchange; heart rate/rhythm measurement; respiration rate/rhythmmeasurement; moisture change sensing; temperature change sensing;thermal expansion; cavitation including void fraction sensing;multi-flow phase change sensing; pulse deinterleaving; jet engineturbine vibrations; pulse source association; MIMO radar targetassociation; seismology; interference suppression; imaging of biologicaltissue; multi-modal imaging; communications; ground penetrating radar;thermal expansion; structure integrity; acoustic vibrometry; railroadtrack health monitoring; music composition reconstruction; instrumenttuning; contaminant detection in food production lines; frequencydehopping; structure monitoring; electronic warfare; and a whole host ofother applications.

Unlike a spectrum analyzer, which typically incorporates a single inputRF port and monitors the time-varying power spectrum of the signalreceived on the single port, the analyzer 800 requires a minimum of tworeceiver input ports. These two receiver channels are phase coherent andcan exhibit gain and phase matching across the frequency range of theinstrument.

The analyzer 800 includes a housing 840 which contains a receiver (e.g.,520, as shown in FIG. 5A). The receiver has at least two input ports850, and preferably at least four input ports. The receiver input ports850 provide signals to the coherent processing channels of the receiver520. The receiver input ports 850 can be connected to two or moreexternal antenna outputs. The antennas can be provided in any of theconfigurations shown in FIG. 2, 3A, 4A, or 5A. Additional antennaconfigurations are also possible. In some embodiments, the analyzer 800includes a user input module which allows the user to specify theconfiguration of the antennas connected to the receiver input ports 850(e.g., dual polarization, space-separated, space-separated dualpolarization, etc.). Based on the number and configuration of connectedantenna inputs, the analyzer 800 can determine which signal pairs toform and analyze. For example, the signal pairs can be any of thoseillustrated in FIG. 3B, 4B, or 5D. In other embodiments, the receiverinput ports 850 can be connected to intermediate frequency signals orbaseband signals.

The housing 840 of the analyzer 800 can also contain a transmitter(e.g., 510, as shown in FIG. 5A). The transmitter 510 has at least oneoutput port 860. (As illustrated, the transmitter 510 and/or thereceiver 520 can be implemented as removable modules.) In someembodiments, the transmitter 510 has two, four, or more output ports860. The transmitter output ports 860 can be connected to one or moretransmitting antennas. In some embodiments, the analyzer 800 includes auser input module which allows the user to specify the configuration ofthe antennas connected to the transmitter output ports 860.

The analyzer 800 can also include one or more displays 880. These candisplay coherent signal dispersion curves on spheres and othervisualization aids. The analyzer 800 can also include one or more userinput elements 870, such as buttons, knobs, etc. The user input elements870 can be used to control various user-selectable options, such assignal processing parameters, signal analysis functions, outputs, etc.In addition, the analyzer 800 can include an input/output port 890 tocommunicate with peripheral devices. The analyzer 800 can also includeany of the components discussed with respect to the systems disclosedherein. In addition, the analyzer 800 can perform any of the processingfunctions discussed herein.

Embodiments have been described in connection with the accompanyingdrawings. However, it should be understood that the figures are notdrawn to scale. Distances, angles, etc. are merely illustrative and donot necessarily bear an exact relationship to actual dimensions andlayout of the devices illustrated. In addition, the foregoingembodiments have been described at a level of detail to allow one ofordinary skill in the art to make and use the devices, systems, etc.described herein. A wide variety of variation is possible. Components,elements, and/or steps may be altered, added, removed, or rearranged.While certain embodiments have been explicitly described, otherembodiments will become apparent to those of ordinary skill in the artbased on this disclosure.

The systems and methods described herein can advantageously beimplemented using, for example, computer software, hardware, firmware,or any combination of software, hardware, and firmware. Software modulescan comprise computer executable code for performing the functionsdescribed herein. In some embodiments, computer-executable code isexecuted by one or more general purpose computers. However, a skilledartisan will appreciate, in light of this disclosure, that any modulethat can be implemented using software to be executed on a generalpurpose computer can also be implemented using a different combinationof hardware, software, or firmware. For example, such a module can beimplemented completely in hardware using a combination of integratedcircuits. Alternatively or additionally, such a module can beimplemented completely or partially using specialized computers designedto perform the particular functions described herein rather than bygeneral purpose computers. In addition, where methods are described thatare, or could be, at least in part carried out by computer software, itshould be understood that such methods can be provided oncomputer-readable media (e.g., optical disks such as CDs or DVDs, harddisk drives, flash memories, diskettes, or the like) that, when read bya computer or other processing device, cause it to carry out the method.

A skilled artisan will also appreciate, in light of this disclosure,that multiple distributed computing devices can be substituted for anyone computing device illustrated herein. In such distributedembodiments, the functions of the one computing device are distributedsuch that some functions are performed on each of the distributedcomputing devices.

While certain embodiments have been explicitly described, otherembodiments will become apparent to those of ordinary skill in the artbased on this disclosure. Therefore, the scope of the invention isintended to be defined by reference to the claims and not simply withregard to the explicitly described embodiments.

What is claimed is:
 1. A method for analyzing a characteristic of atransmitter, a receiver, or a propagation channel, the methodcomprising: obtaining at least one receiver signal resulting from atleast one transmitter signal that has propagated from the transmitter tothe receiver through the propagation channel; forming at least a firstsignal pair which comprises a first receiver signal and a firsttransmitter signal, or first and second receiver signals which areobtained from spatially-separated receiver antennas, or first and secondreceiver signals which are attributable to different transmittersignals; determining amplitude and phase information of a plurality offrequency components for each signal in the first signal pair;determining a set of comparison values for the first signal pair bycomparing respective frequency component phases or respective frequencycomponent amplitudes of the signals in the first signal pair; andanalyzing a characteristic of the set of comparison values.
 2. Themethod of claim 1, further comprising coherently receiving the first andsecond receiver signals, whether they are attributable to a commontransmitter signal or different transmitter signals.
 3. The method ofclaim 2, wherein coherently receiving the first and second receiversignals comprises frequency down-converting the first and secondreceiver signals using a common local oscillator.
 4. The method of claim2, wherein coherently receiving the first and second receiver signalscomprises performing synchronous digital sampling of the first andsecond receiver signals.
 5. The method of claim 1, wherein the first andsecond receiver signals, whether attributable to a common transmittersignal or different transmitter signals, are obtained using co-polarizedportions of one or more receiver antennas.
 6. The method of claim 1,wherein the first and second receiver signals, whether attributable to acommon transmitter signal or different transmitter signals, are obtainedusing orthogonally-polarized portions of one or more receiver antennas.7. The method of claim 1, wherein the first and second receiver signalsare respectively attributable to first and second transmitter signals,and wherein the first and second transmitter signals are separable. 8.The method of claim 7, wherein the separable first and secondtransmitter signals are coherently synthesized.
 9. The method of claim7, wherein the separable first and second transmitter signals overlap intime.
 10. The method claim 7, wherein the separable first and secondtransmitter signals are sent using orthogonally-polarized portions of acommon transmitter antenna.
 11. The method claim 7, wherein theseparable first and second transmitter signals are sent usingspatially-separated transmitter antennas.
 12. The method of claim 1,wherein the first signal pair comprises the first receiver signal andthe first transmitter signal, and wherein the first receiver signal isattributable to a second transmitter signal.
 13. The method of claim 1,wherein comparing respective frequency component phases or respectivefrequency component amplitudes of the signals in the first signal paircomprises calculating Jones vectors or Stokes parameters.
 14. The methodof claim 1, wherein analyzing a characteristic of the set of comparisonvalues comprises identifying a characteristic of a curve formed from thecomparison values at a given time or identifying a time-varying changein the comparison values.
 15. The method of claim 1, wherein the atleast one receiver signal and the at least one transmitter signalcomprise radio frequency (RF) signals, and where the propagation channelcomprises a multipath propagation channel.
 16. A system comprising: twoor more receiver input ports and signal channels for obtaining two ormore receiver signals resulting from at least one transmitter signalthat has propagated through a propagation channel; and a processorconfigured to form at least a first signal pair which comprises a firstreceiver signal and a first transmitter signal, or first and secondreceiver signals which are obtained from spatially-separated receiverantennas, or first and second receiver signals which are attributable todifferent transmitter signals; determine amplitude and phase informationof a plurality of frequency components for each signal in the firstsignal pair; determine a set of comparison values for the first signalpair by comparing respective frequency component phases or respectivefrequency component amplitudes of the signals in the first signal pair;and analyze a characteristic of the set of comparison values.
 17. Thesystem of claim 16, further comprising circuitry to coherently receivethe two or more receiver signals.
 18. The system of claim 17, whereinthe circuitry comprises a common local oscillator to frequencydown-convert the two or more receiver signals.
 19. The system of claim17, wherein the circuitry comprises one or more analog-to-digitalconverters to perform synchronous digital sampling of the two or morereceiver signals.
 20. The system of claim 16, wherein the two or morereceiver input ports and signal channels are substantially gain andphase matched or compensated.
 21. The system of claim 16, furthercomprising one or more receiver antennas coupled to the two or morereceiver input ports and signal channels.
 22. The system of claim 21,wherein the one or more receiver antennas are dual polarized.
 23. Thesystem of claim 16, further comprising a transmitter to transmit the atleast one transmitter signal.
 24. The system of claim 23, wherein thetransmitter comprises two or more transmitter signal channels and outputports to transmit two or more transmitter signals.
 25. The system ofclaim 24, wherein the transmitter comprises circuitry to coherentlysynthesize the two or more transmitter signals.
 26. The system of claim25, wherein the circuitry comprises a common local oscillator tofrequency up-convert the two or more transmitter signals.
 27. The systemof claim 24, wherein the two or more transmitter signal channels andoutput ports are substantially gain and phase matched or compensated.28. The system of claim 16, wherein the system comprises a benchtopanalyzer.
 29. The system of claim 1, wherein the processor is configuredto compare respective frequency component phases and respectivefrequency component amplitudes of the signals in the first signal pairby calculating Jones vectors or Stokes parameters.
 30. The system ofclaim 1, wherein the processor is configured to analyze a characteristicof the set of comparison values by identifying a characteristic of acurve formed from the comparison values at a given time or identifying atime-varying change in the comparison values.